SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 16 ft less than the length of the ladder. How high up the side of the building

Algebra ->  Equations -> SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 16 ft less than the length of the ladder. How high up the side of the building      Log On


   

Question 1002659: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 16 ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 2 ft less than the length of the ladder?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
This is a Pythagorean right triangle problem
a^2 + b^2 = c^2
Let the length of the ladder be x.
One side is x - 16.
The other side is x - 2.
Thus
(x-16)^2 + (x-2)^2 = x^2
x^2-32x+256+x^2-4x+4 = x^2
2x^2 - 36x + 260 = x^2
x^2 - 36x + 260 = 0
(x-26)(x-10) = 0
x = 26 or x = 10
But x cannot be ten since one leg is 16 less.
So the length of the ladder is 26 feet and the distance up the wall is
24 feet.